Common Core State Standards Content Area: Algebra Grade Level: High school Domain: Reasoning with Equations and Inequalities Cluster: Solve equations and inequalities in one variable Standard 4: Solve quadratic equations and in one variable.
b: Solve quadratic equations by inspection (e.g., for x^2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a+-bi for real numbers a and b.
What understandings are desired?
Students will understand that:(U)
• there are multiple was to solve a quadratic equation for an unknown variable.
• the quadratic equation can be applied in the real world.
• the quadratic equation can give complex numbers.
What essential questions will be considered?
Essential Questions:(Q)
• how can a quadratic be solved for an unknown?
• how does the quadratic equation apply to the real world?
• why does the quadratic formula sometimes result in complex numbers.
What key knowledge and skills will students acquire as a result of this unit?
Students will know:(K)
Students will be able to:(S)
• terminology: equation, variable, coefficient, constant, distribute, complex number,
imaginary number, roots, parabola, quadratic, factoring.
• formulas: ax^2+bx+c, quadratic formula, order of operations.
• real life experience: ball trajectory, distance, time, height, length.
• derive a complex number from the quadratic equation.
• represent a complex number in an equation.
• solve a quadratic equation.
• analyze a quadratic in a real life situation.
• consider that a quadratic equation applies to the real world.
• be aware of the multiple ways to solve a quadratic equation.
Stage 1 - Identify Desired Results
Content Area: Algebra
Grade Level: High school
Domain: Reasoning with Equations and Inequalities
Cluster: Solve equations and inequalities in one variable
Standard 4: Solve quadratic equations and in one variable.
b: Solve quadratic equations by inspection (e.g., for x^2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a+-bi for real numbers a and b.
What understandings are desired?
• the quadratic equation can be applied in the real world.
• the quadratic equation can give complex numbers.
What essential questions will be considered?
• how does the quadratic equation apply to the real world?
• why does the quadratic formula sometimes result in complex numbers.
What key knowledge and skills will students acquire as a result of this unit?
imaginary number, roots, parabola, quadratic, factoring.
• formulas: ax^2+bx+c, quadratic formula, order of operations.
• real life experience: ball trajectory, distance, time, height, length.
• represent a complex number in an equation.
• solve a quadratic equation.
• analyze a quadratic in a real life situation.
• consider that a quadratic equation applies to the real world.
• be aware of the multiple ways to solve a quadratic equation.
2004 ASCD and Grant Wiggins and Jay McTighe.